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S.H. Ahmadpanahi
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Surface texturing is one of the main techniques to enhance light absorption in solar cells. In thin film devices, periodic texturing can be used to excite the guided resonances supported by the structure. Therefore, total absorption is enhanced largely due to the excitation of these resonances. Although the maximum absorption enhancement limit in both bulk and photonic structures is known already, the weight of each resonance type in this limit is not yet clear. In this contribution, we extend the temporal couple-mode theory, deriving a closed formula to distinguish the contribution of Fabry-Perot and wave-guided modes within the absorption limit for 1-D grating structures. Secondly, using this analytical approach, we can clearly address cases of bulk and thin absorber thicknesses. Our results, supported by rigorous electromagnetic calculation, show that absorption enhancement in a 1-D grating structure can be much higher than the nano-photonic limit (2πn) reported by Yu et al. Thirdly, beyond the framework put forward by Yu et al., we extended our theory to describe the absorption enhancement in double side textured slabs. We have found that when the periods of top and bottom gratings are aliquant, absorption is enhanced in a wider frequency range. We provide rigorous numerical calculations to support our theoretical approach.
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Surface texturing is one of the main techniques to enhance light absorption in solar cells. In thin film devices, periodic texturing can be used to excite the guided resonances supported by the structure. Therefore, total absorption is enhanced largely due to the excitation of these resonances. Although the maximum absorption enhancement limit in both bulk and photonic structures is known already, the weight of each resonance type in this limit is not yet clear. In this contribution, we extend the temporal couple-mode theory, deriving a closed formula to distinguish the contribution of Fabry-Perot and wave-guided modes within the absorption limit for 1-D grating structures. Secondly, using this analytical approach, we can clearly address cases of bulk and thin absorber thicknesses. Our results, supported by rigorous electromagnetic calculation, show that absorption enhancement in a 1-D grating structure can be much higher than the nano-photonic limit (2πn) reported by Yu et al. Thirdly, beyond the framework put forward by Yu et al., we extended our theory to describe the absorption enhancement in double side textured slabs. We have found that when the periods of top and bottom gratings are aliquant, absorption is enhanced in a wider frequency range. We provide rigorous numerical calculations to support our theoretical approach.
Periodic texturing is one of the main techniques to enhance light absorption in thin-film solar cells. The presence of periodicity, such as grating, allows the excitation of guided modes in the structure, thus enhancing absorption. However, grating efficiency in exciting guided modes is highly dependent on the wavelength and incident angle of light. This is relevant especially in solar cells application, where the light source - the sun - is broadband and largely angle-dependent. Nevertheless, most of literature only focuses on the frequency response of periodic texturing, thus neglecting the effect of angular movement of the sun. In this work we use Fourier expansion to calculate the absorption of each type of mode (guided and non-guided) in an absorptive periodic waveguide. The structure is illuminated with TM and TE polarized light and under three different incident angles. Using this method, we are able to calculate the contribution of a guided resonance to total absorption for different angles of incidence. The work here developed and supported by rigorous numerical calculations can be used to better understand light propagation in a periodic waveguide structure, such as thin-film solar cells.
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Periodic texturing is one of the main techniques to enhance light absorption in thin-film solar cells. The presence of periodicity, such as grating, allows the excitation of guided modes in the structure, thus enhancing absorption. However, grating efficiency in exciting guided modes is highly dependent on the wavelength and incident angle of light. This is relevant especially in solar cells application, where the light source - the sun - is broadband and largely angle-dependent. Nevertheless, most of literature only focuses on the frequency response of periodic texturing, thus neglecting the effect of angular movement of the sun. In this work we use Fourier expansion to calculate the absorption of each type of mode (guided and non-guided) in an absorptive periodic waveguide. The structure is illuminated with TM and TE polarized light and under three different incident angles. Using this method, we are able to calculate the contribution of a guided resonance to total absorption for different angles of incidence. The work here developed and supported by rigorous numerical calculations can be used to better understand light propagation in a periodic waveguide structure, such as thin-film solar cells.
This thesis is structured in six distinct chapters. In Chapter 1 a general introduction is given to address the main challenge in thin-film silicon solar cells and to motivate the need for light trapping. This chapter also describes the main focus of this thesis and the urge to understand the light behaviour inside a periodic waveguide thin film. This is followed by Chapter 2, which provides the mathematical background and the frame work which has been used throughout the thesis. This chapter presents some practical details and calculation techniques which have been used to obtain our result. In Chapter 3, a semi-analytical approach is introduced to calculate the contribution of guided and nonguided resonances to total absorption of a grating waveguide structure under normal incidence. In this approach, we use Fourier expansion to calculate the energy spectral density of the electric field inside the absorber. In this way, the weight of each resonance in total absorption is defined for a large wavelength range for TM and TE polarization. Additionally, the proposed mathematical model is supported by numerical and rigorous calculations, using a software based on the finite element method. This approach is extended for oblique incidence in Chapter 4. In this chapter it is explained howthe variation of tangential and normal components for TM electric field under oblique incidence influences the accuracy of numerical calculation. The correlation between the density of modes and the absorption peaks due to guided mode excitation is also presented in this chapter. Chapter 5 focuses on calculating the maximum absorption enhancement achieved by each type of resonance in a waveguide structure with symmetric and asymmetric gratings. In this chapter a different approach is introduced to count the number of resonances in a grating waveguide structure, at each frequency. Then, temporal coupledmode theory is used to calculate the maximum absorption enhancement for each diffraction order. This approach is extended for a thin film with double-side texturing. Chapter 6 provides the conclusion of the thesis.
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This thesis is structured in six distinct chapters. In Chapter 1 a general introduction is given to address the main challenge in thin-film silicon solar cells and to motivate the need for light trapping. This chapter also describes the main focus of this thesis and the urge to understand the light behaviour inside a periodic waveguide thin film. This is followed by Chapter 2, which provides the mathematical background and the frame work which has been used throughout the thesis. This chapter presents some practical details and calculation techniques which have been used to obtain our result. In Chapter 3, a semi-analytical approach is introduced to calculate the contribution of guided and nonguided resonances to total absorption of a grating waveguide structure under normal incidence. In this approach, we use Fourier expansion to calculate the energy spectral density of the electric field inside the absorber. In this way, the weight of each resonance in total absorption is defined for a large wavelength range for TM and TE polarization. Additionally, the proposed mathematical model is supported by numerical and rigorous calculations, using a software based on the finite element method. This approach is extended for oblique incidence in Chapter 4. In this chapter it is explained howthe variation of tangential and normal components for TM electric field under oblique incidence influences the accuracy of numerical calculation. The correlation between the density of modes and the absorption peaks due to guided mode excitation is also presented in this chapter. Chapter 5 focuses on calculating the maximum absorption enhancement achieved by each type of resonance in a waveguide structure with symmetric and asymmetric gratings. In this chapter a different approach is introduced to count the number of resonances in a grating waveguide structure, at each frequency. Then, temporal coupledmode theory is used to calculate the maximum absorption enhancement for each diffraction order. This approach is extended for a thin film with double-side texturing. Chapter 6 provides the conclusion of the thesis.
Periodic texturing is one of the main techniques for light-trapping in thin-film solar cells. Periodicity allows for the excitation of guided modes in the structure and, thus, largely enhances absorption. Understanding how much a guided resonance can increase the absorption is therefore of great importance. There is a common method to understand if an absorption peak is due to the excitation of a guided mode, using dispersion diagrams. In such graphs, a resonance is identified as the intersection of a guided-mode-line of a uniform waveguide (with the same optical thickness as the grating structure) with the center of a Brillouin zone of the grating. This method is unfortunately not reliable when the grating height is comparable with the thickness of the wave-guide, or when the thickness of the wave-guide is much larger than the wavelength. In this work, we provide a novel approach to calculate the contribution of a guided resonance to the total absorption in a periodic waveguide, without using the dispersion diagram. In this method, the total electric field in the periodic structure is described by its spatial frequencies, using a Fourier expansion. Fourier coefficients of the electric field were used to calculate the absorption of each diffraction order of the grating. Rigorous numerical calculations are provided to support our theoretical approach. This work paves the way for a deeper understanding of light behavior inside a periodic structure and, consequently, for developing more efficient light-trapping techniques for solar cells applications.
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Periodic texturing is one of the main techniques for light-trapping in thin-film solar cells. Periodicity allows for the excitation of guided modes in the structure and, thus, largely enhances absorption. Understanding how much a guided resonance can increase the absorption is therefore of great importance. There is a common method to understand if an absorption peak is due to the excitation of a guided mode, using dispersion diagrams. In such graphs, a resonance is identified as the intersection of a guided-mode-line of a uniform waveguide (with the same optical thickness as the grating structure) with the center of a Brillouin zone of the grating. This method is unfortunately not reliable when the grating height is comparable with the thickness of the wave-guide, or when the thickness of the wave-guide is much larger than the wavelength. In this work, we provide a novel approach to calculate the contribution of a guided resonance to the total absorption in a periodic waveguide, without using the dispersion diagram. In this method, the total electric field in the periodic structure is described by its spatial frequencies, using a Fourier expansion. Fourier coefficients of the electric field were used to calculate the absorption of each diffraction order of the grating. Rigorous numerical calculations are provided to support our theoretical approach. This work paves the way for a deeper understanding of light behavior inside a periodic structure and, consequently, for developing more efficient light-trapping techniques for solar cells applications.
Total electric field in a periodic thin-film structure is described by its Fourier coefficients. These coefficients can be used to calculate the share of different resonances in total absorption in the structure.
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Total electric field in a periodic thin-film structure is described by its Fourier coefficients. These coefficients can be used to calculate the share of different resonances in total absorption in the structure.